A point P is 26 cm away from the centre O of a circle and the length

Question:

A point P is 26 cm away from the centre O of a circle and the length PT of the tangent drawn from P to the circle is 10 cm. Find the radius of the circle.

Solution:

Let us put the given data in the form of a diagram.

We have to find OT. From the properties of tangents we know that a tangent will always be at right angles to the radius of the circle at the point of contact. Therefore $\angle O T P$ is a right angle and triangle $O T P$ is a right triangle.

 

We can find the length of $T P$ using Pythagoras theorem. We have,

$O T^{2}=O P^{2}-T P^{2}$

$O T^{2}=26^{2}-10^{2}$

$O T^{2}=(26-10)(26+10)$

$O T^{2}=16 \times 36$

 

$O T^{2}=576$

$T P=\sqrt{576}$

 

$T P=24$

Therefore, the radius of the circle is 24 cm.

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